To determine the equation of the line in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept, you can use the given information:

• Slope $m = -\frac{1}{3}$
• Y-intercept $b = 1$ (because the y-intercept is at $(0, 1)$)

Now, substitute these values into the slope-intercept form equation:

$y = -\frac{1}{3}x + 1$

So, the equation of the line is:

$y = -\frac{1}{3}x + 1$

Would you like further details or have any questions about this solution?

Here are 5 related questions to expand your understanding:

1. What does the slope of a line tell us about its direction?
2. How do you convert the equation of a line from slope-intercept form to standard form?
3. What would the graph of this line look like?
4. How do you find the x-intercept of this line?
5. What happens to the equation if the slope changes to a positive value?

Tip: The slope $m$ determines how steep the line is and whether it rises or falls. A negative slope means the line goes downwards as you move from left to right.